Similar with the case of CNNs, we can also check the metric and the curvature of the manifold of the coupled networks. Roughly we are now working with the direct product of the manifold of each subsystem with the tangent spaces of the subsystems as orthogonal subspaces of the tangent space of the complete manifold. This is very similar with the case of the semi-direct group product in the metamorphsis framework in the template matching system[1]}. It can be expected that the structure of the manifold is much more complex than the relatively simple CNN case. But if the curvature of each subsystem's manifold is almost negative as in the quantum computation, then the convergence of the training of the coupled system naturally will be more difficult, just as indicated in the case of neural Turing machines.
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